Question

In a car lift, compressed air exerts a force on a piston with a radius of 2.62 cm. This pressure is transmitted to a second piston with a radius of 10.8 cm. a) How large a force must the compressed air exert to lift a 1.44 × 104 N car

Answer 1

847.45 N

Step-by-step explanation:

F₁=force of exerted by smaller piston

F₂=force of exerted by larger piston=1.44×10⁴ N

A₁=Area of smaller piston= 2.62 cm =0.0265 m

A₂=Area of larger piston= 10.8 cm =0.108 m

Pressure exerted by both the pistons will be equal

`P_1=P_2\\\Rightarrow (F_1)/(A_1)=(F_2)/(A_2)\\\Rightarrow F_1=(F_2)/(A_2) A_1\\\Rightarrow F_1=(14400)/(\pi*  0.108^2)\pi*  0.0262^2\\\Rightarrow F_1=847.45\ N`

Hence, force exerted to lift a 14400 N car is 847.45 N